Average Error: 0.0 → 0.0
Time: 8.8s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(z, x, \left(1 - x\right) \cdot y\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(z, x, \left(1 - x\right) \cdot y\right)
double f(double x, double y, double z) {
        double r466176 = 1.0;
        double r466177 = x;
        double r466178 = r466176 - r466177;
        double r466179 = y;
        double r466180 = r466178 * r466179;
        double r466181 = z;
        double r466182 = r466177 * r466181;
        double r466183 = r466180 + r466182;
        return r466183;
}
↓
double f(double x, double y, double z) {
        double r466184 = z;
        double r466185 = x;
        double r466186 = 1.0;
        double r466187 = r466186 - r466185;
        double r466188 = y;
        double r466189 = r466187 * r466188;
        double r466190 = fma(r466184, r466185, r466189);
        return r466190;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[y - x \cdot \left(y - z\right)\]

Derivation

  1. Initial program 0.0

    \[\left(1 - x\right) \cdot y + x \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1 - x, y, x \cdot z\right)}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(x \cdot z + 1 \cdot y\right) - x \cdot y}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(z, x, \left(1 - x\right) \cdot y\right)}\]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z, x, \left(1 - x\right) \cdot y\right)\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (- y (* x (- y z)))

  (+ (* (- 1 x) y) (* x z)))